Topological remarks on end and edge-end spaces

[2404.17116] Topological remarks on end and edge-end spaces Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2404.17116 (math) [Submitted on 26 Apr 2024 ( v1 ), last revised 15 Apr 2026 (this version, v3)] Title: Topological remarks on end and edge-end spaces Authors: Leandro Fiorini Aurichi , Paulo Magalhães Júnior , Lucas Real View a PDF of the paper titled Topological remarks on end and edge-end spaces, by Leandro Fiorini Aurichi and 1 other authors View PDF HTML (experimental) Abstract: The notion of ends in an infinite graph $G$ might be modified if we consider them as equivalence classes of infinitely edge-connected rays, rather than equivalence classes of infinitely (vertex-)connected ones. This alternative definition yields the edge-end space $\Omega_E(G)$ of $G$, in which we can endow a natural (edge-)end topology. For every graph $G$, this paper proves that $\Omega_E(G)$ is homeomorphic to $\Omega(H)$ for some possibly another graph $H$, where $\Omega(H)$ denotes its usual end space. However, we also show that the converse statement does not hold: there is a graph $H$ such that $\Omega(H)$ is not homeomorphic to $\Omega_E(G)$ for any other graph $G$. In other words, as a main result, we conclude that the class of topological spaces $\Omega_E = \{\Omega_E(G) : G \text{ graph}\}$ is strictly contained in $\Omega = \{\Omega(H) : H \text{ graph}\}$. Comments: 17 pages, 1 figure. V3 contains no longer a game-theoretical approach to a previous result on the theory of end spaces Subjects: Combinatorics (math.CO) ; General Topology (math.GN) MSC classes: 05C63, 54H99, 05C40, 06A07 Cite as: arXiv:2404.17116 [math.CO] (or arXiv:2404.17116v3 [math.CO] for this version) https://doi.org/10.48550/arXiv.2404.17116 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Lucas Real [ view email ] [v1] Fri, 26 Apr 2024 02:15:18 UTC (33 KB) [v2] Thu, 2 May 2024 01:56:29 UTC (33 KB) [v3] Wed, 15 Apr 2026 12:51:53 UTC (25 KB) Full-text links: Access Paper: View a PDF of the paper titled Topological remarks on end and edge-end spaces, by Leandro Fiorini Aurichi and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2024-04 Change to browse by: math math.GN References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• The Separable Quotient Problem and the Lotz Property in Banach Spaces#1155519
• Universal approximation of continuous maps between topological vector spaces#1110341
• Linking invariants of spatial graphs#616992
• Linking invariants of spatial graphs#616492
• The Walk-Length Filtration for Persistent Homology on Weighted Directed Graphs#179190